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  1. Abstract The theory of topological modular forms (TMF) predicts that elliptic genera of physical theories satisfy a certain divisibility property, determined by the theory’s gravitational anomaly. In this note we verify this prediction in Duncan’s supermoonshine module, as well as in tensor products and orbifolds thereof. Along the way we develop machinery for computing the elliptic genera of general alternating orbifolds and discuss the relation of this construction to the elusive “periodicity class” of TMF. 
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  2. A bstract We revisit from a modern bootstrap perspective the longstanding problem of solving QCD in the large N limit. We derive universal bounds on the effective field theory of massless pions by imposing the full set of positivity constraints that follow from 2 → 2 scattering. Some features of our exclusion plots have intriguing connections with hadronic phenomenology. The exclusion boundary exhibits a sharp kink, raising the tantalizing scenario that large N QCD may sit at this kink. We critically examine this possibility, developing in the process a partial analytic understanding of the geometry of the bounds. 
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  3. null (Ed.)